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      Atmospheric and topographic 
      correction of multitemporal Landsat TM imagery 
 Zhang Yugui
 The Research Institute of Forest 
      resource Information
 Chinese Academy of Forestry
 
 Abstract
 The paper briefly introduced a developing 
      system for comprehensive correction satellite imagery. Standarized 
      reflectance images were produced by atmospheric correction, topographic 
      correction, sensor calibration etc. The atmospheric parameters parameters 
      were interpolated by using local meteorological records. The path radiance 
      derived from visual range is adjusted with dark pixels in the image data. 
      A digital topographic model was used both to correct for the 
      georadiometric effects and to monitor the optical thickness. The 
      normalized reflectance image were enhanced with linear or non-linear 
      transformation. A set of multitemporal subscenes of four dates in 
      Trolleba, Sweden were used as examples to illustrate the good 
      correspondence of correction results in quite different atmospheric 
      conditions.
 
 Introduction
 The main factors that seriously 
      affect the radiometric quality of digital satellite data are atmospheric 
      attenuation and topographic distortion, in addition to sensor variation. 
      All these factors are related to and restrictive with each other. 
      Therefore, a correction algorithm that considers only a single digital 
      topographic model. The paper described a developing correction system 
      which made comprehensive correction of Landsat TM and other satellite 
      data, including sensor calibration, path radiance evaluation, the 
      calculation of attenuation coefficients of atmosphere, the variations of 
      direct solar illumination and diffuse illumination caused by topography, 
      as well as minor modifications of the components of optical thickness due 
      to calculate the needed atmospheric parameters by using metrological 
      records, and presented result ofthe calculation after these parameters 
      were input to the radiative transfer model of Turner.
 
 The 
      multitemporal TM images used in this study consist of 4 subscenes of 400 X 
      400 pixels of the same Trollebo scene, located in south-central part of 
      sweden. The elevation of the area is from 164 to 285 meters ASL. Clear 
      water bodies are scattered over the whole area. The trollebo area contains 
      mainly forest lands with a small portion of agricultural fields. The four 
      dates constitute the whole growing season of forest vegetation , Pine, 
      spruce , birch and broadleaves make up the major forest type categories. 
      Table 1 listed the data of the 4 dates.
 
 Table 1. Parameters for trollebo subscence. The scene 
      center coordinates,
 sun elevation azimuth and view angles are in 
      decimal degrees.
 
 
        
        The correction 
      procedures
          | Scene | Over pass time | scene center coordinates | sun azim | sun elev | view angle | Sun-earth dist. (au) |  
          | 1 | 194/20:2 1984.4.27 09 35 39 | (57.317,14.756) | 133.42 | 39.17 | 2.058 | 0.9932 |  
          | 2 | 194/20:2 1984.5.13 09 36 12 | (57.819,14.718) | 131.47 | 43.47 | 2.733 | 0.9794 |  
          | 3 | 193/20 : 1984.7.09 09 27 05 | (57.317,15.713) | 123.88 | 44.98 | 1.324 | 0.9670 |  
          | 4 | 193/20:2 1984.9.0209 39 38 | (57.317,14.493) | 136.92 | 33.66 | 2.987 | 0.9827 |  Conceptually, the reflectance images can be obtained 
      through three sequential linear transformations. 
       
        Evaluation and computation of atmospheric parametersA Transformation From Digital Numbers (DN) To observed Spectral 
        Radiance Values (Lobs) This is accomplished by using published 
        radiance calibration constants (Barker 1987), which is usually termed 
        absolute calibration. Spectral radiance and irradiance were used in the 
        study instead of in-band units throughout the computation procedures to 
        facilitate comparison between sensor (Price 1987).
 
 The 
        Lobs can be obtained by
 
 Lobs = 
        DN* (Lmax - Lmin) / 255 
        +Lmin ----------------(1)
 
 Lmax - 
        Lmin are constants representing the radiance at DN= 0 and 
        DN=255, respectively. These constants may vary with date, ground 
        receiving and processing station. Before this tranformation, a relative 
        compensation calobration between etectors were performed for most 
        scenes.
 
 
A Transformation From Radiance Lobs to Spectral 
        Reflectance RIt is complicated and critical. The assumption of a 
        Lambertian scattering behaviour for most targets would simplify the view 
        angle effect as only differential atmospheric effect. Therefore, the 
        correction of main interest is atmospheric and topographic corrections, 
        illumination and view angle corrections, in addition to sensor 
        calibration. The radiance observed by a sensor in a given band can be 
        expressed as
 
 Lobs = 1 / p 
        (Eo cosi Exp(-t/cosqo) +gEd)R Exp(-t/cosqv ) +Lp ------(2)
 
 or in a 
        simplified form
 
 Lobs = 1/ p 
        R Eg Tv +Lp
 
 and the transformed reflectance R for a 
        target can be expressed as
 
 R= p 
        (Lobs- Lp ) / Eg Tv) ..............(3)
 
 The meanings of various factors are defined as follows:
 
 Lobs = radiance observed at the sensor 
        (mWcm-2 Sr-1)
 
 1 / p = The bidirectional reflectance distribution 
        function (BRDF) for a Lambertian surface
 
 Eo= solar irradiance at 
        the top of the atmosphere (m Wcm-2),
 
 Eo was calibrated 
        with published solar exoatmospheric spectral irradiances in TM bands
 
 Eo was calibrated with published solar exoatmospheric spectral 
        irradiances in TM bands
 
 i= solar incidence angle with respect to 
        surface normal
 
 t= atmospheric extinction coefficient (optical 
        thickness)
 
 qo, qv = solar zenith angle and observation 
        zenith angle
 
 g = a geometric factor taking into account of the 
        part of sky radiance not contributing in the illumination of inclined 
        terrain , g= 0.5+0.5coss, s=terrain slope angle
 
 Ed = 
        diffuse sky irradiance on a horizontal surface (m Wcm-2) Ed 
        is modified by atmosphere and topography.
 
 Eg= (Eo 
        cosi Tq+g Ed) = global irradiance on the 
        surface (m Wcm-2)
 
 Tq = 
        exp(-t/cosqo) = atmospheric downward 
        transmittance
 
 Tv = Exp (-t/ cosqv) = atmospheric up eard transmittance
 
 Lp = path radiance from multiple scattering (m Wcm-2 
        sr-1 )
 
 This reflectance tranformation involves the 
        approximation of some varibles by using different methods according to 
        parameters available . Combining equation (1) and (3) we obtain
 
 R= p / (Eg Tv) *(DN(Lmax - 
        Lmin) / 255 +Lmin -Lp) -----(3a)
 
 
A Transformation of R to an Eight-bit Digital Number 
        (DN')It may be a linear or non-linear transformation, 
        incorporating appropriate contrast stretch between predefined minimum 
        and maximum reflectance limits Rmax - and Rmin
 
 DN' = 255 F[(R-Rmin) / (Rmax - 
        Rmin)] ................(4)
 
 The linear 
        transformation is convenient if the enhanced reflectance images are to 
        undergo further processing, but for the hard copy products, a non-linear 
        transformation can be applied to TM bands. The square root function 
        increases the contrast of low reflectance portion, and compress the 
        contrast of high reflectance portion (Ahern 1989).
 
 Although each 
        step involves much consideration and techniques, the second step 
        requires more investigation and exploration. The actual scattering 
        properties of natural surfaces differ from the Lambertian assumption to 
        varying extent (Teillet et al. 1982) The diffuse approximation is more 
        likely to be valid for terrain slopes of less than 25 degrees and 
        effective illumination angles of less than 45 degrees (Smith et al. 
        1980) or further less (Cavayas 1987). In our study, the solar zenith 
        angle exceeded these limits, which may cause a system error of the 
        reflectance values. Since we have no sufficient knowledge about the BRDF 
        for natural targets, such assumption is the only convenient solution at 
        present, espescially for forest canopy complexities which are considered 
        to be Lambertian surface in small solar zenith angle.
 The global irradiance Eg , diffuse irradiance 
      Ed  and path radiance Lp  for the center wavelength of 
      TM bands were calculated with the Turner and Spencer (1972) reductive 
      transfer model, and with Forster's modification (1984) for the computation 
      of the single scattering phase function, after appropriate TM band 
      adjustment. This requires estimated or calculated optical thickness 
      t,solar zenith qo  solar azimuth, nadir 
      view angle qv  , view azimuth as input. 
      The scene center coordinates and scene center overpass time were used to 
      derive the components of optical thickness t. The radiative transfer model 
      provided convenience for establishing relationship between atmospheric 
      parameters. In the process of computing the parameters, the scale heights 
      for Ed , Eg  and Lp  were determined, which 
      facilitate the computation procedures of corresponding values for each 
      pixel. 
       
        The 
      double usage of topographic modelThe Estimation of Path Radiance 
        LpLp is an important factor. In our study, 
        it was derived from radiative transfer model after computation of the 
        input meteorological data. However, several approaches can be applied to 
        evaluate Lp for the purpose of reference. Since clear water 
        bodies exist in the studied area, the dark pixel method (Ahern 1977) was 
        used due to its simplicity . The relative scattering function method 
        (chavez 1987 , 1988) is also convenient . The covariance matrix method 
        (Switzer 1981) and RIM ( Crippen 1987) require that spectrally 
        homogeneous targets being distributed over slopes of various aspects. In 
        this study, the Lp values were used to compare with those calculated by 
        using meteorological data, and to monitor and adjust the latter if they 
        were unreliable.
 
 
Use of Local metrological records to Estimate optical 
        ThicknessThe optical thickness t in equation (1) is a critical 
        coefficient and is affected by many factors. since the measurement of at 
        overpass time is seldom done, it is usually estimate some atmospheric 
        various methods meteorological records could be utilized to estimate 
        some atmospheric parameters. The daily records at 1,7,13 and 19 hours 
        include temperature, air pressures, water vapour pressure, relative 
        humidity, visibility, wind speed etc. The overpass time data were 
        derived from the interpolated data. The physical atmospheric thickness 
        was accounted for as function of topographic elevation. There fore the 
        station elevation ASL (above sea level) and the parameter values at the 
        station elevation were used to derive the scale heights of parameters, 
        which were applied to each pixel of the image when a topographic model 
        was available. The normal optical thickness t equals the sum of the 
        attenading coefficients, and they are independent. Therefore t is made 
        up of Rayleigh component tr due to molecular scattering, aerosol 
        component tp due to particle scattering, and components due to selective 
        absortption of gases, such as water wapour component tw, 
        ozone component toz, and carbon dioxide component tco2. All 
        these are wavelength dependent.
 
 t = tr + 
        tp + tw + toz + tco2 
        +.......(5)
 
 we deal with the t components separately. The Rayeigh 
        molecular scattering is regarded as of dry air, and the water absorption 
        as of partial pressure of water vapour, and the aersol scattering as of 
        suspending particles.
 
 The visibility may be a measure of tp for 
        a particular vertical distribution . Turner (1972) graphed tp as a 
        function of visibility for continental atmosphere. We have interpolated 
        and extrapolated the graphs for TM bands with the central wavelength as 
        reference, and then an adjustment or alignment can be applied to the 
        interpolated tp values with shaded clear water pixel values 
        in TM band 4 as reference in the process of calculation.
 The inclusion of even a rough 
      elevation data could decisively help to stress the difference of the 
      physical thickness of the atmosphere and consequently help to adjust the 
      optical thickness components tr  tp  and tw  
      for each pixel as well as to monitor the changes of the scaleheights of 
      Eg  Ed  and Lp  with the elevation of each 
      pixel. A course topographic model as we have used would help to modify and 
      improve the enhanced reflectance images to 3-4 counts.  The 
      coarseness of spatial and quantization resolution of the DTM data may not 
      help to raise the correction accuracy for rugged mountain area, since the 
      slope the slope-aspect geometry is not a Gaussian distribution (Teillet 
      1986). The digital elevation data used in this experiment were created by 
      digitizing contour lines of the UTM map sheet at 1:50 000 scale and 
      linearly interpolated between contour lines. The terrain slope s and 
      aspect a can be derived with reference to the neibouring pixels. The solar 
      incidence angle to the surface normal is expressed by:  cosi 
      =cosqo  coss +sin qo sincos(fo -a) s= terrain slope , a = terrain 
      aspect (azimuth) There are three optional applications for the 
      elevation data in the algorithms: 
       
        Result and discussionIn absence of elevation data the average elevation of the subscene 
        as well the elevation of the reference water bodies are used. 
 
when a coarse elevation model is available and the topography is 
        rather complicated used for the adjustment of the optical thickness and 
        illumination conditions for each pixel.
 
when accurate elevation data could be obtained or the areas of 
        internet are not so complicated as to demand an accurate topographic 
        model it is worth to transfer the data in to a slope aspect format and 
        both the optical thickness and illumination geometry expressed by cosi 
        and g could be considered in our study after such correction the mean 
        square of spectral features of the some targets were reduced by about 
        30%. The aerosol content, its 
      thickness and distribution atmosphere are the main problem atmospheric 
      correction .The visibility codes 1,2,4 indicates the stability of 
      atmosphere at the time of the observation and the tp and Lp values hence 
      obtained were quite reliable but the adjustment tp are over estimated the 
      zero reflectance pixels were not exactly found because of negligence of 
      wind speed and diffuse irradiance on the water interpreted due to partial 
      shading of the pixels date 3 had pixel values approached and the 
      interpreted visibility is only 7.5 Km the adjustment of dark pixel values 
      approached the real value and improved the result for a clear stable 
      atmosphere the visual range codes seemed to be more reliable but if the 
      recorded visual ranges changed abruptly the dark pixel helped to approach 
      the real value than interpolated value. 
      Table 2. The extroatmospheric solar irradiance 
      Eo are sin earth distance adjusted. The global spectral 
      irradiance Eg diffuse spectral irradiance Ed and spectral 
      path radiance Lp* are the values at sea level the 
      scale
 heights of Eg* Ed Lp are also 
      justed with the pixel respectively
 
 
        
        
          | Parameter | TM1 | TM2 | TM3 | TM4 | TM5 | TM7 |  
          | date 1 (4/27) |  
          | Eo(mWcm-2um-1) | 193.21 | 180.57 | 153.72 | 103.36 | 21.65 | 7.35 |  
          | Eg(mWcm-2um-1) | 106.03 | 102.49 | 91.11 | 62.61 | 12.81 | 4.45 |  
          | Ed(mWcm-2um-1) | 27.03 | 21.49 | 16.22 | 9.24 | 1.30 | 0.38 |  
          | Lp*(**um-1sr-1) | 1.1814 | 0.4247 | 0.1811 | 0.1213 | 0.0099 | 0.0019 |  
          | Lp*(**um-1sr-1) | 1.9415 | 0.7823 | 0.3619 | 0.2623 | 0.0261 | 0.0052 |  
          | Egscale(m) | -38569 | -50997 | -65349 | -89163 | -101761 | -127130 |  
          | Edscale(m) | 1754 | 1542 | 1439 | 1366 | 1283 | 1267 |  
          | Lp Scale(m) | 1482 | 1384 | 1341 | 1395 | 1287 | 1265 |  
          | date 2 (5/13) |  
          | Eo(mWcm-2um-1) | 191.67 | 179.14 | 152.49 | 102.54 | 21.47 | 7.49 |  
          | Eg (mWcm-2um-1) | 115.77 | 111.43 | 98.80 | 67.38 | 13.61 | 4.76 |  
          | Ed (mWcm-2um-1) | 31.55 | 24.93 | 18.68 | 10.53 | 1.46 | 0.43 |  
          | Lp(**um-1sr-1) | 1.7235 | 0.6813 | 0.3016 | 0.2514 | 0.0208 | 0.0039 |  
          | Lp*(**um-1sr-1) | 2.1155 | 0.8612 | 0.3887 | 0.3241 | 0.0277 | 0.0053 |  
          | Egs scale (m) | -40923 | -53979 | -68640 | -92234 | -91231 | -117572 |  
          | Edscale (m) | 1806 | 1576 | 1461 | 1381 | 1289 | 1271 |  
          | Lp Scale(m) | 1459 | 1372 | 1406 | 1406 | 1294 | 1270 |  
          | date 3 (7/9) |  
          | Eo(mWcm-2um-1) | 189.23 | 176.86 | 150.55 | 101.24 | 21.20 | 7.20 |  
          | EgmWcm-2um-1) | 117.20 | 112.71 | 99.85 | 65.76 | 12.37 | 4.50 |  
          | EdmWcm-2um-1) | 39.74 | 31.85 | 23.89 | 13.36 | 1.72 | 0.53 |  
          | Lp(**um-1sr-1) | 5.4500 | 2.1598 | 0.8805 | 0.9670 | 0.0480 | 0.0071 |  
          | Lp*(**um-1sr-1) | 2.6805 | 1.0984 | 0.4522 | 0.5544 | 0.0269 | 0.0039 |  
          | Egscale(m) | -36276 | -46297 | -56874 | -69934 | -49391 | -66263 |  
          | Edscale(m) | 1837 | 1609 | 1492 | 1424 | 1328 | 13.01 |  
          | Lp Scale(m) | 1302 | 1267 | 1228 | 1424 | 1319 | 1278 |  
          | date 4 (9/2) |  
          | Eo (mWcm-2um-1) | 192.31 | 179.73 | 153.00 | 102.89 | 21.55 | 7.32 |  
          | Eg (mWcm-2um-1) | 91.18 | 88.86 | 79.27 | 52.92 | 10.20 | 3.67 |  
          | Ed (mWcm-2um-1 | 17.01 | 13.43 | 10.12 | 5.81 | 0.74 | 0.22 |  
          | Lp (**um-1sr-1 | 1.1681 | 0.4255 | 0.1659 | 0.1785 | 0.0077 | 0.0011 |  
          | Lp* (**um-1sr-1) | 1.4018 | 0.5345 | 0.2173 | 0.2373 | 0.0110 | 0.0015 |  
          | Eg scale(m) | -39656 | -54371 | -70899 | -83554 | -63013 | -86801 |  
          | Ed scale(m) | 1661 | 1465 | 1375 | 1348 | 1272 | 1255 |  
          | Lp scale(m) | 1670 | 1509 | 1392 | 1457 | 1286 | 1254 |  Table 2 listed the sea 
      level values of Ed  and Eg  and Lp  and 
      their scale heights diffuse spectral irradiance Ed  and spectral 
      path radiance Lp  will decrease with elevation while the global 
      spectral irradiance Eg  increases with elevation. The 
      introduction of scale height for these three parameters simplified the 
      computation of their modification due to elevation variation it has been 
      examined that error committed by using scale height method is only one per 
      thousand compared with applying more complicated algorithms.  Clear 
      lakes of relative stable reflectance were selected for comparison of 
      correction result the obvious atmospheric between original counts were 
      greatly compressed(Table 3). 
      Table 3. Comparison of original values and corrected 
      reflectance for relative stable object (clear lakes) 
 
        
        
          |  | TM1 | TM2 | TM3 | TM4 | TM5 | TM7 |  
          | average original counts |  
          | date 1 | 53.8 | 16.6 | 11.5 | 9.2 | 4.7 | 3.6 |  
          | date 2 | 57.7 | 18.2 | 13.7 | 10.6 | 6.1 | 3.8 |  
          | date3 | 63.5 | 19.7 | 15.9 | 11.4 | 7.2 | 3.9 |  
          | date 4 | 41.1 | 13.5 | 9.4 | 6.3 | 3 | 3.0 |  
          | Corrected reflectance |  
          | date 1 | 0.0539 | 0.425 | 0.0266 | 0.0000 | 0.0001 | 0.0000 |  
          | date 2 | 0.533 | 0.414 | 0.0266 | 0.0000 | 0. 0000 | 0.0000 |  
          | date 3 | 0.549 | 0.0403 | 0.0259 | 0.0000 | 0.0000 | 0.0000 |  
          | date 4 | 0.0556 | 0.0401 | 0.273 | 0.0000 | 0.0000 | 0.0000 |  The following conclusion 
      can be derived from this study: 
       
        ReferencesThe comprehensive correction to remotely sensed data for atmospheric 
        and georadiometric distortion is feasible the converted reflectance 
        stable reflectance objects showed an excellent conformity how ever the 
        degree of correction accuracy on the precision of the input data if a 
        even radioactive transfer model and a precise correction equation are 
        used.
 
The meteorological record could be used to estimate the components 
        of optical thickness and to make clear distribution of both direct solar 
        and diffuse irradiance the path radiance Lp should be estimated by using 
        multiple methods for comparison since the visibility observation in 
        comparison among transfer models is also beneficial.
 
A georadiometric correction may be an option if a reliable digital 
        terrain model is not available such a model could be used for both 
        adjusting the topography dependent atmospheric coefficients and for 
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For the enhancements of reflectance images the forest reflectance 
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      Science. |